I guess it depends on what you wish to livestream. 
See how we go about it by reading the Github to the Jukebox: https://github.com/LightningJukeboxBot/LightningJukeboxBot?tab=readme-ov-file#a-bitcoin-enabled-jukebox

In particular the part to OBS: https://github.com/LightningJukeboxBot/LightningJukeboxBot?tab=readme-ov-file#a-bitcoin-enabled-jukebox

You can use https://vdo.ninja to capture various image/audio/text/chat sources to import and compose into one vid.feed via OBS to stream to wherever.

We stream to zap.stream which you can find in Amethyst client for mobile to tune into or via any web-browser.

If you want to stream to multiple destinations, get the relevant plugin (read jukebox github readme)